Erdős–Ko–Rado Theorems: Algebraic Approaches: 149 (Cambridge Studies in Advanced Mathematics, Series Number 149) - Hardcover

Godsil, Christopher; Meagher, Karen

Hardcover

ISBN 10: 1107128447 ISBN 13: 9781107128446

Publisher: Cambridge University Press, 2015

Synopsis

Aimed at graduate students and researchers, this fascinating text provides a comprehensive study of the Erdos-Ko-Rado Theorem, with a focus on algebraic methods. The authors begin by discussing well-known proofs of the EKR bound for intersecting families. The natural generalization of the EKR Theorem holds for many different objects that have a notion of intersection, and the bulk of this book focuses on algebraic proofs that can be applied to these different objects. The authors introduce tools commonly used in algebraic graph theory and show how these can be used to prove versions of the EKR Theorem. Topics include association schemes, strongly regular graphs, the Johnson scheme, the Hamming scheme and the Grassmann scheme. Readers can expand their understanding at every step with the 170 end-of-chapter exercises. The final chapter discusses in detail 15 open problems, each of which would make an interesting research project.

About this title

Review:

'This is an excellent book about Erdos-Ko-Rado (EKR) Theorems and how to prove them by algebraic methods ... The writing style is reader-friendly, and proofs are well organized and easily followed. Also, every chapter contains Exercises and Notes, which are very useful for expanding understanding and finding further reading. The reviewer recommends this book without hesitation to all graduate students and researchers interested in combinatorics.' Norihide Tokushige, MathSciNet

Book Description:

The Erdős–Ko–Rado Theorem is a fundamental result in combinatorics. Aimed at graduate students and researchers, this comprehensive text shows how tools from algebraic graph theory can be applied to prove the EKR Theorem and its generalizations. Readers can test their understanding at every step with the end-of-chapter exercises.

About this edition

• Publisher: Cambridge University Press
• Publication date: 2015
• ISBN 10: 1107128447
• ISBN 13: 9781107128446
• Binding: Hardcover
• Number of pages: 350